Whakaoti i te 105^n=700

$$105 ^ { n } = 700$$

Whakaoti mō n

$$n=\log_{105}\left(700\right)\approx 1.407635614$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakamahia ngā ture taupū me ngā taupū kōaro hei whakaoti i te whārite.

$$105^{n}=700$$

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

$$\log(105^{n})=\log(700)$$

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

$$n\log(105)=\log(700)$$

Whakawehea ngā taha e rua ki te \log(105).

$$n=\frac{\log(700)}{\log(105)}$$

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$n=\log_{105}\left(700\right)$$

Whakaoti mō n (complex solution)

$$n=\frac{2\pi n_{1}i}{\ln(105)}+\log_{105}\left(700\right)$$

$$n_{1}\in \mathrm{Z}$$